In this paper, Lindberg provided a redescription of dengizicus from India. At the end of this redescription, he discussed Kiefer's previous assignment of this species to Kiefer's subgenus Metacyclops, and wrote that

"The animals having the article of the fifth foot strongly broadened, bearing a well-developed inner spine and a long outer seta, inserted far from each other due to the width of the article, thereby presenting a configuration so aberrant from the other animals assigned to the subgenus Metacyclops of Kiefer that it appears quite messy to maintain them among these, because it is exactly the fifth foot that serves as a basis for the establishment of the different subgenera of the genus Cyclops. Gurney has previously remarked on this failure of logic. In order to continue the use of Greek prefixes, I propose the term Apocyclops to designate the new subgenus in which it is appropriate to group the 3 species known to the present with a fifth foot resembling that of C. dengizicus Lepechkine, the two others being C. (A.) panamensis Marsh and C. (A.) royi Lindberg."

(my translation. Reference: Lindberg, K. 1942. Cyclopides (Crustacés Copépodes) de l'Inde. XIV. Notes sur quelques membres du sous-genre Metacyclops Kiefer. Records of the Indian Museum 44 (2): 139-190. text on pp. 140-142)
You can see by this wording that Lindberg did not designate a type species for Apocyclops.
Lindberg raised Apocyclops to genus level in 1954, but neither then nor in subsequent papers on this group did he (or anybody else) ever designate a type. However, since that time, authors have accepted the oldest species (dengizicus) as the type.
written by Janet W. Reid, March 2016[details]